Heat a large wok or frying pan over high heat. Add vegetable oil, swirling pan to coat. Sprinkle steak with cornstarch, mixing to distribute evenly, then add to hot oil. Cook, stirring as little as needed for even browning, until meat is browned, 7 to 10 minutes. Transfer to a plate.
Add 1 tbsp. sesame oil to wok, followed by ginger, chiles, and asparagus. Cook until fragrant, about 3 minutes. Stir in soy sauce, sugar, and broth. Cook until mixture comes to a simmer, about 4 minutes. Return steak to wok, stirring once just to combine, and let sauce thicken slightly.
Put cooked noodles on a serving plate. Drizzle with 1 tsp. sesame oil; toss to coat. Spoon steak mixture over noodles.